irule redirect without changing host on client

Just guessing here, but you're CSS is likely being referenced from the client directly as "/application/something.css", in which case I think your first iRule can use a minor tweak:

when HTTP_REQUEST { 
    switch [string tolower [HTTP::uri]] { 
        "/my/application/*" { 
            pool application_pool 
            HTTP::uri [string range [HTTP::uri] 3 end ] 
        }
        "/application/* {
            pool application_pool
        } 
        "/test/other/*" { 
            pool test_pool 
            HTTP::uri [string range [HTTP::uri] 5 end ] 
        } 
        default { 
            pool other_pool 
        } 
    } 
}